Word of caution, REW is right on but beware of the current going through the meter. Most have a fuse,some do not. My fluke handles 10 amps, easily enough for this test, until you accidentally try to turn the engine over, if so say goodbye to the fuse in the meter or your meter if not fused. Using an amp clamp most likely won't be accurite enough. Anything over .3 amps will be enough draw to kill the battery.
At least I think its .3 amps and under is okay, that is like the computers, if you have them and the radio memory, someone correct me if .3 is wrong, its late!

This is interesting. I don't see where the OP said anything about having a charger on the batteries while in storage. Perhaps he did. Didn't say how old the batteries are either. Definitely didn't say what the state of charge was when he took them out of storage except to say it was fully charged. How did he know that? Perhaps that battery is shot. Maybe? I bet the arching was there at the end of last season too, same circuits drawing down the power as before without killing the battery though. Bad battery I think.

Joker,
On many boats, the manufacturer installs a master switch to kill all battery draw from any thing on the boat.

But normally, this does not include the motor.

So, on many boats there is a pair of heavy motor wires that run to the motor. Then, there is a pair of 8 or 10 gauge wires that run from the battery to the boats, fuse block. In cases like these, the 8 or 10 gauge wire runs from the battery to the master power switch, and then to the fuse and switch block. So, when the term Master Switch is used, it normally refers to cutting the power that is feeding the boat and its accessories.
The master switch and does not normally cut the connection from the on board charger to the batteries, which is normally another wire that is connected separately to the battery/ies.

Another place to look is if you have a older GPS with a external antena,
some of them have a power lead of there own run back to the battery.
I had this happen to me. I would have to unplug the fuse if i was not going to use the boat for a week or two.
Good Luck

This spring mine did the same thing. My battery was warranted by Interstate so I took it over to them. They said they would put it on their charger with 5 other batteries. They said it would probably take 3 days to charge it. After 5 days they called and said it was ready and that it was taking a full charge and holding under load. I asked why this was and they could not give me a good answer. They did say that they see this kind of thing alot and that the battery is often times still good and many people just assume it has went bad. I havent had a problem with it in the last 4 trips with all electronics and livewell pumps running it seems to be functioning fine.

This is interesting. I don't see where the OP said anything about having a charger on the batteries while in storage. Perhaps he did. Didn't say how old the batteries are either. Definitely didn't say what the state of charge was when he took them out of storage except to say it was fully charged. How did he know that? Perhaps that battery is shot. Maybe? I bet the arching was there at the end of last season too, same circuits drawing down the power as before without killing the battery though. Bad battery I think.

My thoughts also - without knowing original conditions, I would wonder if the batteries sat all winter without being charged or on trickle. Might have even been run down before being stored. The very first thing for him to do would be to put them on a charger, fully charge, and then see what happens ....

Ok, might not of been 100% clear...I know the big motor has a minimal draw and maybe my kicker does to for that matter...I do believe however from when I hooked the battery up an arc occurred when I hooked up the wires that feed the dash fuse box...I have both the 115 and the kicker hooked to the battery which I know is at full charge. I dont however have a 3 bank charger so leaving the cranking battery charging is not an easy option, its doable, but not easy... Its a Lund Mr Pike boat, and like I said, I think it has to do with the boat, not the motors...I do have a radio, cd, but the only thing it keeps a small small amount of power for the internal clock, otherwise all power to the radio is killed with the master switch as well...Any help now that Ive cleared it up a bit.

I have a Pro Angler, which I am led to believe is the tiller version of the Mr. Pike, and I know that my gauges are powered by the main wiring, not through the ignition switch. I have mine plugged in when not on the water so I don't have to reset the radio by disconnecting the main all the time. I do know on mine, it will draw down in about 5 days if not run or on the charger.

My dealer told me that the master switch should kill everthing on your boat. The reason being that if your charger should fail and feed 120 volts into your electric system most,if not all of your electrical items would be fried.